Numerical analysis of a pseudo-compact C-N conservative scheme for the Rosenau-KdV equation coupling with the Rosenau-RLW equation

Boundary value problems

Xintian Pan¹  Luming Zhang¹  Yiju Wang² 

[1] School of Management, Qufu Normal University, Rizhao, China;School of Mathematics and Information Science, Weifang University, Weifang, China

关键词: Rosenau-KdV-RLW equation;    conservative scheme;    existence;    convergence;    stability;   

DOI  :  10.1186/s13661-015-0328-2

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, numerical solutions for the Rosenau-KdV equation coupling with the Rosenau-RLW equation are considered and a new C-N pseudo-compact conservative numerical scheme, which preserves the original conservative properties is designed. The proposed scheme is based on a finite difference method. The existence of the difference solutions has been shown by the Brouwer fixed point theorem. Unconditional stability, second-order convergence, and a prior error estimate of the scheme are proved by the discrete energy method. Numerical examples have been given to verify the theoretical results.

【 授权许可】

CC BY